Media captionRussell Holly, who works for technology website geek.com, says his phone has bent

Twitter users have also posted thousands of comments about the claims, using the hashtag Bentgate.

The BBC has contacted Apple but the firm has yet to provide any comment.

One industry watcher said the company should investigate the complaints and issue a statement as soon as possible.

Image copyrightMacrumorsImage caption
This photo was posted to MacRumors by Devin Pitcher, who said it showed a friend's bent iPhone

"I think initially they should acknowledge the situation," said Jasdeep Badyal, an analyst from the telecoms consultancy CCS Insight.

"Then the second step will be to take action by providing cases or replacements."

He added that even if it emerged that there had been a "faulty batch" or there was only a minor risk of damage, the firm should still issue a statement to make this clear.

But Chris Green, principal technology analyst at the advisory service Davies Murphy Group, thought that Apple should take a different tack.

"This is not an issue that Apple - or other phone companies - need to be compelled to respond to or fix. If anything this is a reflection of how people have started to use devices beyond what they were designed for," he said.

Image copyrightMacrumorsImage caption
This image was posted to MacRumors by a user nicknamed iBoost621

"Even the most recent smartphones are not designed to be put in trouser pockets - front or back - where they are going to be under the most chassis strain. And this just illustrates the fact that the public's desire for manufacturers to strive for ever thinner and lighter devices means that we are getting ever more fragile devices.

"Just casually sticking a £700 smartphone in your pocket is an increasingly reckless thing to do."

'Serious issue'

Apple is marketing both the iPhone 6 and the larger iPhone 6 Plus as the thinnest smartphones it has released - with both models less than 0.3in (0.76cm) thick.

Image copyrightRussell HollyImage caption
Russell Holly's phone no longer sits flat on a table when placed on its front, but is less warped than iPhones shown in other photos

However, it is unusual for the issue to be given so much attention so soon after a launch - the new iPhones went on sale only on Friday.

Russell Holly, who writes about mobile phones for Geek.com, said that, having looked into the reports, he was surprised to find he had become a victim of the phenomenon.

"I set my phone glass down on a flat surface and noticed the phone wobbled slightly when I pressed on the top right and bottom left corners," he told the BBC.

"I had already taken many photos of this phone for my work at Geek.com and could find no evidence of this warping when the phone was initially removed from the box. Like many of the other reports, I have never dropped the phone or abused it in any way.

"The phone sat in my front pocket for a couple of hours the day before while I drove around town to run a few errands, but there's no way that should have caused any damage to the phone.

"This seems like a serious issue that Apple needs to at the absolute least be warning consumers about. Having spent quite a bit of time with many different smartphones, the severity of this issue is unique."

Insurer Square Trade had declared the new iPhones "more durable" than their predecessors after carrying out tests, but did not carry out "bendability" checks.

It's not something people should be particularly worried about, but they should be aware of it and use some common sense.

Earlier iPhone models and phones from other manufacturers will do the same thing when subjected to particular stresses.

With the much larger body of the iPhone 6 Plus in particular, perhaps allowing for additional stress while constrained in the user's pocket, the issue may be somewhat more prevalent, but it's still being overblown.

With millions of units sold already and only a handful of cases reported so far, it's by no means an epidemic.

It seems pretty straightforward to recommend that users not sit on their iPhones in rear pockets and to be mindful of whether their movements are putting stress on devices kept in front pockets.

A rigid case will certainly help support the phone as well.

Damage control

Apple has a tendency not to respond to problems until it can release a definitive statement.

Image copyrightEPAImage caption
Apple made a virtue of the new iPhones' thinness at its press event earlier this month

This was the case in 2010, when its former chief executive Steve Jobs held a news conference after multiple reports that the iPhone 4 dropped calls when gripped on the lower left-hand side.

Mr Jobs announced at the event that buyers of the handset would get a free case to work around the problem.

His successor, Tim Cook, also took time before penning a letter to apologise for problems with the iPhone's Maps app in 2012.

But there are also instances when the firm has opted to respond in a less high-profile manner.